A note on larger orbit size

2020 ◽  
Vol 23 (5) ◽  
pp. 913-916
Author(s):  
Ping Jin ◽  
Yong Yang
Keyword(s):  
Group Theory ◽  
Character Degrees ◽  
Alternating Groups ◽  
Brauer Character ◽  
Small Defect ◽  
Orbit Size ◽  
Open Question

AbstractIn this note, we present an improvement on the large orbit result of Halasi and Podoski, and then answer an open question raised in [X. Chen, J. P. Cossey, M. Lewis and H. P. Tong-Viet, Blocks of small defect in alternating groups and squares of Brauer character degrees, J. Group Theory 20 2017, 6, 1155–1173].

Blocks of small defect in alternating groups and squares of Brauer character degrees

2017 ◽  
Vol 20 (6) ◽  
Author(s):  
Xiaoyou Chen ◽  
James P. Cossey ◽  
Mark L. Lewis ◽  
Hung P. Tong-Viet
Keyword(s):  
Character Degrees ◽  
Alternating Groups ◽  
Brauer Character ◽  
Small Defect

AbstractLet

A Note on Brauer Character Degrees of Solvable Groups

1991 ◽  
Vol 34 (3) ◽  
pp. 423-425 ◽  
Author(s):  
You-Qiang Wang
Keyword(s):  
Solvable Group ◽  
Solvable Groups ◽  
Character Degrees ◽  
Finite Solvable Group ◽  
Prime Integer ◽  
Derived Length ◽  
Brauer Character ◽  
Brauer Characters

AbstractLet G be a finite solvable group. Fix a prime integer p and let t be the number of distinct degrees of irreducible Brauer characters of G with respect to the prime p. We obtain the bound 3t — 2 for the derived length of a Hall p'-subgroup of G. Furthermore, if |G| is odd, then the derived length of a Hall p'-subgroup of G is bounded by /.

scholarly journals Sylow Normalizers and Brauer Character Degrees

2000 ◽  
Vol 229 (2) ◽  
pp. 623-631
Author(s):  
Antonio Beltrán ◽  
Gabriel Navarro
Keyword(s):  
Character Degrees ◽  
Brauer Character

scholarly journals Automating Symmetry-Breaking Calculations

2004 ◽  
Vol 7 ◽  
pp. 101-119 ◽  
Author(s):  
P. C. Matthews
Keyword(s):  
Group Theory ◽  
Symmetry Breaking ◽  
Symmetry Group ◽  
Irreducible Representations ◽  
Symmetry Groups ◽  
Periodic Patterns ◽  
Alternating Groups ◽  
Spatial Symmetry

AbstractThe process of classifying possible symmetry-breaking bifurcations requires a computation involving the subgroups and irreducible representations of the original symmetry group. It is shown how this calculation can be automated using a group theory package such as GAP. This enables a number of new results to be obtained for larger symmetry groups, where manual computation is impractical. Examples of symmetric and alternating groups are given, and the method is also applied to the spatial symmetry-breaking of periodic patterns observed in experiments.

Some conjectures on Brauer character degrees

2020 ◽  
Vol 550 ◽  
pp. 210-218
Author(s):  
Hung P. Tong-Viet
Keyword(s):  
Character Degrees ◽  
Brauer Character

scholarly journals p -Parts of Brauer character degrees

2014 ◽  
Vol 403 ◽  
pp. 426-438 ◽  
Author(s):  
Gabriel Navarro ◽  
Pham Huu Tiep ◽  
Hung P. Tong-Viet
Keyword(s):  
Character Degrees ◽  
Brauer Character

On Huppert's Conjecture for Alternating Groups of Low Degrees

2015 ◽  
Vol 22 (02) ◽  
pp. 293-308 ◽  
Author(s):  
Hung Ngoc Nguyen ◽  
Hung P. Tong-Viet ◽  
Thomas P. Wakefield
Keyword(s):  
Character Degrees ◽  
Simple Groups ◽  
Direct Factor ◽  
Sporadic Groups ◽  
Alternating Groups ◽  
Low Degrees ◽  
Groups Of Lie Type

Bertram Huppert conjectured in the late 1990s that the nonabelian simple groups are determined up to an abelian direct factor by the set of their character degrees. Although the conjecture has been established for various simple groups of Lie type and simple sporadic groups, it is expected to be difficult for alternating groups. In [5], Huppert verified the conjecture for the simple alternating groups An of degree up to 11. In this paper, we continue his work and verify the conjecture for the alternating groups of degrees 12 and 13.

scholarly journals The largest character degrees of the symmetric and alternating groups

2015 ◽  
Vol 144 (5) ◽  
pp. 1947-1960 ◽  
Author(s):  
Zoltán Halasi ◽  
Carolin Hannusch ◽  
Hung Ngoc Nguyen
Keyword(s):  
Character Degrees ◽  
Alternating Groups

scholarly journals On the existence of block-transitive combinatorial designs

2010 ◽  
Vol Vol. 12 no. 1 (Combinatorics) ◽  
Author(s):  
Michael Huber
Keyword(s):  
Information Theory ◽  
Group Theory ◽  
Finite Simple Group ◽  
Group Classification ◽  
Permutation Groups ◽  
Combinatorial Designs ◽  
Coding And Information Theory ◽  
International Audience ◽  
Open Question

Combinatorics International audience Block-transitive Steiner t-designs form a central part of the study of highly symmetric combinatorial configurations at the interface of several disciplines, including group theory, geometry, combinatorics, coding and information theory, and cryptography. The main result of the paper settles an important open question: There exist no non-trivial examples with t = 7 (or larger). The proof is based on the classification of the finite 3-homogeneous permutation groups, itself relying on the finite simple group classification.

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